7(a) (i) Solve the differential equation: \[ \frac{dx}{dt}=\sqrt{x}\sin(t/2) \] to find \(x \) in terms of \(t\).
Well we may observe that this DE is of variables separable type so we may write: \[\int \frac{1}{\sqrt{x}} \; dx = \int \sin(t/2)\; dt \]
We may now integrate to get: \[ \sqrt{x}= -\cos(t/2)+C \] and squaring we get \[x=(C-\cos(t/2))^2\]
Now the remaining parts of this question can be solved by applying the relevant initial conditions etc.
No comments:
Post a Comment